On the minimality of some generating sets of the aggregation clone on a finite chain

Clone theory plays an important role in studying aggregation functions on bounded posets or bounded lattices. Several important classes of aggregation functions on a bounded lattice L form a clone, particularly the set of all aggregation functions on L, the so-called full aggregation clone on L. For any finite lattice L, this clone is known to be finitely generated and various generating sets and their constructions have been presented in recent papers. The aim of this paper is to extend previous results concerning generating sets of aggregation clones on finite chains. Namely, the objective is to discuss the minimality of certain generating bases, the so-called (chi,circle plus)-generating sets. (C) 2021 Elsevier Inc. All rights reserved.